This paper presents a comparison framework to study the relative benefits of the typical trapezoidal method with the lesser-used implicit midpoint method for the simulation of audio lumped systems at a fixed rate. We provide preliminary tools for understanding the behavior and error associated with each method in connection with typical analysis approaches. We also show implementation strategies for those methods, including how an implicit midpoint method solution can be generated from a trapezoidal method solution and vice versa. Finally, we present some empirical analysis of the behavior of each method for a simple diode clipper circuit and provide an approach to help interpret their relative performance and how to pick the more appropriate method depending on desirable properties. The presented tools are also intended as a general approach to interpret the performance of discretization approaches at large in the context of fixed-rate simulation.

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In this paper a new technique is introduced that allows for the variable step-size simulation of wave digital filters. The technique is based on the preservation of the underlying network variables which prevents fluctuation in the stored energy in reactive network elements when the step-size is changed. This method allows for the step-size variation of wave digital filters discretized with any passive discretization technique and works with both linear and nonlinear reference circuits. The usefulness of the technique with regards to audio circuit simulation is demonstrated via the case study of a relaxation oscillator where it is shown how the variable step-size technique can be used to mitigate frequency error that would otherwise occur with a fixed step-size simulation. Additionally, an example of how aliasing suppression techniques can be combined with physical modeling is given with an example of the polyBLEP antialiasing technique being applied to the output voltage signal of the relaxation oscillator.

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